UCRL-JRNL-209412

Numerical Modeling of HohlraumRadiation Conditions: Spatial andSpectral Variations due to SamplePosition, Beam Pointing, and HohlraumGeometry

D. H. Cohen, O. L. Landen, J. J. MacFarlane

February 3, 2005

Physics of Plasmas

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Numerical Modeling of Hohlraum Radiation Conditions: Spatial and Spectral

Variations Due to Sample Position, Beam Pointing, and Hohlraum Geometry

David H. CohenDepartment of Physics and Astronomy, Swarthmore College, Swarthmore, Pennsylvania 19081

Otto L. LandenLawrence Livermore National Laboratory, Livermore, California 94550

Joseph J. MacFarlanePrism Computational Sciences, 455 Science Dr., Suite 140, Madison, Wisconsin 53711

View-factor simulations are presented of the spa-tially varying radiation conditions inside double-endedgold hohlraums and single-ended gold hohlraums (“hal-fraums”) used in inertial confinement fusion (ICF) andhigh energy density (HED) physics experiments [J. Lindl,Phys. Plasmas 11, 339 (2004); M. D. Rosen, Phys.Plasmas 3, 1803 (1996)]. It is shown that in many cir-cumstances, the common assumption that the hohlraum“drive” can be characterized by a single temperature istoo simplistic. Specifically, the radiation conditions seenby an experimental package can differ significantly fromthe wall reemission measured through diagnostic holesor laser entrance holes (LEHs) by absolutely calibrateddetectors. Furthermore, even in situations where theradiation temperature is roughly the same for diagnos-tics and experimental packages, or for packages at differ-ent locations, the spectral energy distributions can varysignificantly, due to the differing fractions of reemittingwall, laser hot spots, and LEHs seen from different loca-tions. We find that the spatial variation of temperature,and especially the differences between what diagnosticslooking in the LEH measure vs. the radiation temper-ature on wall-mounted experimental packages, is gener-ally greater for double-ended hohlraums than it is forhalfraums. View-factor simulations can also be used toexplore experimental variables (halfraum length and ge-ometry, sample position, and beam pointing) that can beadjusted in order to, for example, maximize the radiationflux onto a sample, or other package. In this vein, sim-ulations of hohlraums and halfraums with LEH shieldsare also presented.

I. INTRODUCTION

Optimizing the time- and wavelength-dependenthohlraum radiation drive onto a fuel capsule is a key com-ponent in achieving ignition in inertial confinement fusion(ICF) experiments [1, 2]. Although much experimentaland theoretical effort has been expended in understand-ing the x-ray drive characteristics of hohlraums and opti-mizing the drive symmetry onto the capsule, there havebeen few studies of the spatial variation of the radiationfield conditions within hohlraums, and especially withinhalfraums. The x-ray spectrum incident on a surface in

a hohlraum or halfraum, whether part of the wall, a fuelcapsule, or some other object within the cylinder, willvary with location and orientation of the surface accord-ing to the relative view factors of wall reemission, laserhot spots, and cold laser entrance holes (LEHs) and di-agnostic holes. Detailed view-factor modeling can playan important role in answering questions about this vari-ation, and can be used to interpret diagnostics and planexperiments.

In this paper we will present view-factor models ofhohlraums and halfraums, investigating the spatial vari-ations of the radiation field (both overall intensity andspectral energy distribution), and the effects of halfraumsize and geometry and of beam pointing. One conclusionfrom this modeling is that care must be taken in inferringthe drive onto an experimental package from a measure-ment of wall reemission from a particular direction whenusing an absolutely calibrated detector, such as DANTE[3]. A more general conclusion is that view-factor simula-tions are a valuable tool for optimizing the performanceof hohlraum experiments and in interpreting diagnosticmeasurements.

By their nature, view-factor simulations do not ac-count directly for hydrodynamics, laser-plasma interac-tions, or detailed atomic physics. View-factor calcula-tions are based on power balance among energy sourceterms, radiation losses (absorption), and reemission (re-flection). On the other hand, view-factor simulations pro-vide a reasonable representation of the radiation field dis-tribution throughout a 3-D grid of surfaces, and do so ata small fraction of the CPU costs of multi-dimensionalradiation-hydrodynamics codes. View-factor codes canbe used effectively in estimating hohlraum radiation tem-peratures and predicting the radiation symmetry on ICFcapsules. The simulations we present here are relevantto all but the latest times of laser hohlraum experimentswhen on-axis stagnation of gold plasma contributes sig-nificantly to the radiation properties of a hohlraum andthe associated interpretation of diagnostics.

We will critically examine the standard analytic treat-ment of hohlraum energy balance, in which the radia-tion properties of a hohlraum are described by a sin-gle “hohlraum radiation temperature.” And althoughthe emission from each computational surface element

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in our view-factor simulations is taken to be Planckian,the flux incident on any given surface in a simulation(whether wall, target, or diagnostic) can be distinctlynon-Planckian. We will show examples where deviationsfrom a blackbody spectrum are non-trivial. We beginby benchmarking DANTE measurements of a hohlraumexperiment [4] on OMEGA [5]. We then show that exper-imental packages can be subject to radiation conditionsthat are quite different than those seen by DANTE, evenwhen that diagnostic is used on an optimal LEH-viewingline of sight.

The focus of this study will be on effectively emptyhohlraums and halfraums. However, we do investigatehow the radiation conditions change with the presence ofa capsule in Sec. III. In Sec. IV we explore the funda-mental differences between hohlraums and halfraums, interms of both DANTE measurements and the radiationonto an experimental package. (Note that we use theterms “sample” and “package” interchangeably in thispaper.) Finally, we show how variations in the beampointing and LEH size (Sec. V) and geometry (length,presence of disks or foils near the LEH) of a halfraum,and internal LEH shields in a hohlraum, (Sec. VI) af-fect the interpretation of diagnostics and how they canbe optimized to produce the maximum possible radiationtemperature onto an experimental package.

II. SPATIAL DEPENDENCE OF THE

RADIATION DRIVE IN A HOHLRAUM

We first present the results of simulations of a set ofOMEGA experiments reported on by Decker et al. [4].In these well-characterized experiments, the hohlraumtemperature was inferred by measuring the absolute fluxemitted from a portion of the hohlraum wall. For theseexperiments, ten 42 degree OMEGA beams (Cone 2) andtwenty 59 degree OMEGA beams (Cone 3), having a to-tal energy of 500 J each and with 1 ns square profiles,illuminated a standard (2300 µm length by 1600 µm di-ameter) gold hohlraum, with three-quarter (or 1200 µmdiameter) LEHs. Three-quarter LEHs are used in all themodels we present in this paper, unless otherwise noted.The beam pointing in these experiments and in our mod-eling was such that all 15 beams on each side of thehohlraum made a single ring of hot spots, centered 480µm from the LEH plane. The beams were all focused atthe pointing spot, where they crossed the long hohlraumaxis (at the LEH plane for the Cone 3 beams and 400µm outside of the hohlraum for the Cone 2 beams).

One purpose of the Decker et al. experimental cam-paign was to show that the absolutely calibrated x-ray de-tector, DANTE, gives a better indication of the hohlraumradiation conditions seen by a capsule when it views thewall reemission through the LEH, rather than through adiagnostic hole at the midplane. The hohlraums in theseexperiments were on the P5-P8 axis of the OMEGA tar-get chamber, so that the DANTE viewing angle was 37.4

degrees with respect to the hohlraum axis (see Fig. 1 fora model of the hohlraum target, including the DANTEview of this configuration).

We performed a series of simulations of these hohlraumexperiments on OMEGA using the VISRAD 3-D view-factor code (v3.1) [6]. VISRAD computes the spatially-dependent radiation flux about a 3-D grid of surface el-ements using a steady-state power balance model andmaterial-dependent reflection fractions (albedos). Eachsurface element is treated as a spatially thin, opticallythick Lambertian source with a Planckian frequency de-pendence. Thus, the (non-Planckian) spectrum incidenton a given surface element is composed of contributionsfrom multiple Planckian sources. These contributions tothe radiation flux incident on each surface element aresummed for each surface element over all other sourceelements, accounting for the solid angle of the source asseen from the sample, as well as the incident angle ofthe source radiation onto the sample. See Fig. 2 for asketch showing these geometrical considerations. Notethat the Lambertian flux on the sample is proportionalto cos θ cos φ.

Laser beam energy deposition is computed using re-alistic space- and time-profiles for the beams (includingthe f/6.7 beam effective focal ratio of OMEGA), in con-junction with 3-D ray-trace algorithms for determiningbeam-target intersections. The 3-D ray-trace algorithm,in which each laser beam is sub-divided into a large num-ber of “beamlets,” is used to determine which surface el-ements are hit by a given portion of a laser beam. WhileVISRAD also computes the specular reflection of laserlight off surfaces (glint), laser reflectivities for all surfaceswere assumed to be zero for the simulations describedhere. The target components in the calculation are mod-eled as a discretized grid of surface elements. The time-dependent albedo and x-ray conversion efficiency (XCE)are input parameters. In the simulations discussed be-low, the albedo is based on 1-D radiation-hydrodynamicssimulations of a gold foil exposed to a radiation drive con-sistent with that in the OMEGA experiments.

We note that the view-factor modeling ignores hydro-dynamic motion of the hohlraum walls, as well as non-equilibrium effects, internal energy stored in the walls bythe radiative heating of the object elements, and detailedopacities and emissivities for the hohlraum. This mod-eling also neglects the effect of temperature gradients inthe hohlraum walls, which can lead to a viewing-angle de-pendence of emission temperature. We stress that view-factor codes play a complementary role to atomic andhydrodynamics codes. Our goal here is not to calculatewall motion nor the detailed atomic physics and asso-ciated line spectra. However, the view-factor modelingaccounts for the spatial variation of the radiation condi-tions, and to some extent, the generally non-Planckianspectra in hohlraum environments (via the summationover numerous blackbody surface elements of differenttemperatures). The time variation of the hohlraum radi-ation properties in a VISRAD simulation are computed

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FIG. 1: Hohlraum images generated with the VISRAD view-factor code, relevant to the experiments discussed in reference[4]. The top panel shows the OMEGA beam pointing intothe hohlraum cylinder seen side-on. Note that the Cone 2beams on each side are pulled back so that the beams fromboth cones make a single ring on each side of the hohlraum.The middle panel shows the same target model, but from theposition of the DANTE diagnostic. The lower panel shows theDANTE view again, but with the beams hidden, and with thewall temperature at t = 1.0 ns displayed as a color map (thedynamic range in this, and all other, temperature color mapsshown in the paper is 140 eV to 220 eV). Note the ring oflaser hot spots on each side of the hohlraum. Note also inall of these images how structures in the model seen from theback, or outside, are rendered as transparent mesh to allow foran unobstructed view of the interior of the hohlraum. Thisconvention will be used throughout the paper. Finally, wepoint out that the “front,” DANTE-facing, LEH is in theupper right in this, and all similar figures throughout thepaper.

FIG. 2: Schematic of the view-factor calculation for an ar-bitrary geometry. The flux from any source surface elementonto any other sample surface element is proportional to thecosine of the angle between the line of centers of the two ele-ments and the surface normal of the source element (becausethe source element is assumed to be a Lambertian emitter)and also to the cosine of the line of centers and the normalof the sample element (accounting for the projected cross sec-tion of the sample as seen by the source). The line of centersis indicated by the dashed line while the two surface normalsare indicated by arrows.

by making a series of steady-state calculations, each us-ing appropriate beam powers, x-ray conversion efficien-cies, and albedos.

To model the OMEGA experiments described above,we calculated the radiation onto a surface at the posi-tion of the DANTE diagnostic every 100 ps, using thebeam and hohlraum properties described at the begin-ning of this section. We assumed perfect square pulseswith exactly 1.0 ns duration and 500 J total energy perbeam. We incorporated a simple model of the laser x-rayconversion efficiency, with a linear ramp up to a valueof 0.55 at 200 ps, and a constant value thereafter. Here,the x-ray conversion efficiency refers to the fraction ofincident laser power that is converted to x-ray radiation.The remainder of this energy is converted into kinetic orinternal energy, or can be lost to the system via laser scat-tering. In our view-factor calculations, the partitioningof this non-radiative energy is not modeled.

For the gold albedo, we use the results of a 1-D, time-dependent hydrodynamics simulation of gold reemissionof x-rays. The albedo value peaks at 0.73 at 1 ns, for aconstant power drive reaching approximately 190 eV. InFig. 3 we show the assumed XCE and calculated albedo

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along with the modeled DANTE temperatures and theDANTE data obtained by Decker et al. [4]. Note thatour modeling reproduces the observed DANTE data atall times well within the 6% errorbars on the data. Thesesimulations do not include a capsule, in order to facili-tate comparisons to an equivalent halfraum. In the nextsection we show that the presence of a capsule simplylowers the calculated radiation temperature and does soquite uniformly, so that there is effectively a degeneracybetween the presence of a capsule and an increase in theXCE.

In Fig. 3 we also show the time-dependent radiationtemperature on the hohlraum wall at the midplane. Itis significantly (∼ 15 eV) lower than the DANTE tem-perature. This is due to the less favorable view factorof laser hot spots from the midplane wall compared toDANTE, but mainly due to the contribution from thecold LEHs. In various hohlraum experiments, some typeof sample, or other package, is placed at the hohlraummidplane, to expose it to the radiation drive. Historically,hohlraum radiation conditions have also been diagnosedfrom midplane wall reemission flux [7–9], which is equalto the midplane wall incident radiation multiplied by thealbedo. Clearly, hohlraum radiation diagnostic resultswill vary depending on the location of the wall reemis-sion they sample. Thus, while DANTE measurementsthrough the LEH provide valuable data on the hohlraumradiation characteristics, they do not provide a directmeasure of the radiation field seen by an experimentalpackage. The differences between the wall temperaturesseen by DANTE and the radiation drive temperaturesseen by a package can be ∼ 7− 8%. This means that theradiation flux (Frad =

∫∞

0Fνdν = σT 4

R; note that “ra-diation temperature,” TR, is defined by this equation),and therefore the energy absorbed by the experimentalpackage, can be different by ∼ 30 − 35% compared towhat would be inferred using the DANTE measurementdirectly.

It is useful to compare these detailed calculations tothe simpler, and more traditional, analytic power bal-ance treatment. Using ηPL = Prad = ((1 − α)Awall +ALEH)σT 4

R (see, for example, eqn. 1 in ref. [7]) and avalue of η = 0.55 for the XCE, we find at t = 1.0 ns whenthe albedo is α = 0.73, a value of TR = 192 eV for the“hohlraum radiation temperature.” This, as expected,is somewhat less than the DANTE temperature, both inour modeling (202 eV) and in the experiments (201 eV),since DANTE, unlike any point inside the hohlraum, doesnot see any of the cold LEH regions. It is very close tothe radiation temperature on the sample (191 eV, for awall-facing sample at the center of the hohlraum, 190 eVfor an LEH-facing sample, and 188 eV for a wall-mountedsample), as expected. Note that increasing the XCE toη = 0.69 gives an analytic hohlraum temperature thatagrees with the DANTE temperature at t = 1.0 ns. Thishigher value of the XCE is in better agreement with thevalues that are usually assumed [7].

It is interesting also to compare the spectral energy

FIG. 3: The top panel shows the assumed x-ray conversion ef-ficiency (dashed line) and calculated albedo (solid line), usedas inputs to the view-factor simulations, the results of whichare shown in the lower panel. In the lower panel, the filledsquares with error bars are the DANTE temperature measure-ments from ref. [4] while the open squares are the simulatedDANTE temperatures from the view-factor calculations. Thecircles are the simulated radiation temperatures at the mid-plane wall of the hohlraum.

distribution of the radiation incident on the midplane tothat measured by DANTE. In Fig. 4 we show the simu-lated DANTE spectrum at t = 1.0 ns along with that in-cident on the midplane hohlraum wall. For reference, wealso show the equivalent blackbody spectra (the Planck-ian spectra having the same integrated power, or radia-tion temperature, as the calculated spectra). Note that

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FIG. 4: The simulated DANTE spectrum (solid black) alongwith the equivalent blackbody spectrum (dashed black) fort = 1.0 ns in the VISRAD hohlraum simulation and the sim-ulated spectrum incident on the hohlraum wall at the mid-plane (solid gray) along with its equivalent blackbody spec-trum (dashed gray) from the same simulation time. Note thatthe radiation temperatures are 202 eV for DANTE and 188eV for the midplane wall.

both spectra are harder than the equivalent blackbodyspectra, and that this effect is somewhat stronger for themidplane, where the significant view factor of cold LEHsreplacing part of the wall leads to a deficit of low-energyphotons.

Of course, the differences between the DANTE(through the LEH) and midplane radiation conditionswill depend on beam pointing. In general, the fartherin the pointing, the stronger the radiation will be at thehohlraum midplane. This is due both to the hot spotsbeing closer to the midplane and less radiation escapingout the LEHs. The situation for the DANTE looking inthe LEH is more complicated, and depends on the rel-ative fraction of the sky occupied by laser hot spots, asseen from DANTE’s position. To investigate this, weperformed two additional simulations, identical to theone presented above, except for the beam pointing. Inthe first variation, the ten Cone 2 beams are pointed400 µm farther into the hohlraum, giving a mean laserspot position 620 µm from the LEH plane (we refer tothis pointing as “nominal” throughout this paper). Likethe Cone 3 beams, they are pointed at the center of theLEH, which creates a second ring of five hot spots oneither side of the hohlraum, closer to the midplane thanthe single ring in the initial simulations, which have amean spot position 480 µm from the LEH plane. In thesecond variation, all 30 beams are pointed an additional200 µm farther into the hohlraum, giving a mean spotposition of 820 µm from the LEH plane.

FIG. 5: The DANTE views of the hohlraum in the two caseswith different beam pointings (top two panels). As in thebottom panel of Fig. 1, we show a color map of emission tem-perature at t = 1.0 ns, and hide the beams for clarity. Thecolor scale spans 140 eV to 220 eV, and as is true for all thecolor figures throughout the paper, it is identical to the mapshown at the bottom of Fig. 1. The lower panel shows thetrends of DANTE temperature (squares) and midplane tem-perature (circles) as the beam pointing is changed. The filledsymbols represent simulation time t = 1.0 ns (XCE = 0.55and albedo = 0.73) and the open symbols represent simula-tion time t = 100 ps (XCE = 0.28 and albedo = 0.18). Theoriginal model, used to reproduce the experiments reportedon in [4], has a mean laser spot position 480 µm from the LEHplane. The first variation (620 µm) is shown in the top paneland the second variation (820 µm) is shown in the middlepanel. We note that in this last case, the Cone 2 beams fromeither side of the hohlraum hit the wall almost exactly at themidplane, creating a single, combined ring of hot spots.

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In Fig. 5 we show the results of this series of simulationswith varying beam pointings. The radiation drive tem-perature onto the midplane wall does, in fact, increaseas the beam pointing moves farther in the hohlraum to-ward the midplane. The DANTE temperature increasesalmost as much, but for a different reason, as the pointingmoves inward and hence out of the partial occlusion ofthe lip. As in the original simulations, these hohlraums’LEHs have 75% the hohlraum diameter, and thus haveannular lips. The lip certainly can affect the DANTEview of hot spots and wall reemission, which we explorein the context of halfraums in Sec. V. In closing, wenote that the trends shown here are very similar whenwe look at earlier times, where both the albedo and theXCE are lower than at 1 ns. The only notable differenceis a greater similarity between the DANTE and sampletemperatures for the deepest pointing at early times, ascan be seen in the lower panel of Fig. 5.

III. EFFECTS OF A CAPSULE

A spherical fuel capsule located at the center of thehohlraum acts as another sink of photons (due to the rel-atively low albedo of the plastic capsule) and will lowerthe hohlraum temperature accordingly. To explore thenature and magnitude of this effect, we repeated the an-alytic hohlraum radiation temperature calculation with a520 µm diameter spherical capsule in the hohlraum, andthen we repeated two of the view-factor simulations dis-cussed above, but with a capsule. We assumed a capsulealbedo of α = 0.3 independent of time, and also assumedthat the capsule size remained constant over the 1.0 nsduration of the simulation.

The hohlraum temperature calculation discussed inthe previous section was modified to include the areaof the capsule: ηPL = Prad = ((1 − α)Awall + ALEH +(1 − αcap)Acap)σT 4

R. To calculate the hohlraum radia-tion temperature at t = 1.0 ns, we used η = 0.55 forthe XCE and α = 0.73, as we did previously, while thecapsule albedo was assigned a value of αcap = 0.3. Forthese values, we find that the capsule’s presence lowersthe hohlraum radiation temperature by 4 eV to TR = 188eV at t = 1.0 ns.

We repeated two of the numerical view-factor simula-tions: one with the “single ring” pointing used in theDecker et al. experiments (corresponding to Fig. 1) andthe other with the “nominal” pointing in which all thebeams are pointed at the middle of the LEH (correspond-ing to the upper right-hand panel of Fig. 5). In Fig. 6we show the results of these two new simulations, whichdo, indeed, show lower radiation temperatures than thecorresponding simulations without capsules.

In Fig. 7 we compare the time-dependent radiationtemperature from each simulation. At t = 1.0 ns, theDANTE temperature is 5 eV lower with the capsule inthe case of the “nominal” pointing (202 eV vs. 206 eV)and 6 eV lower for the “single ring” pointing (196 eV

FIG. 6: VISRAD simulations of hohlraums without (left) andwith (right) fuel capsules. The capsules are centered in thehohlraums and have a diameter of 520 µm and an albedo ofα = 0.3. The top two panels show the “single ring” pointingwhile the bottom two panels show the “nominal” pointing inwhich two rings are formed by pointing both the Cone 2 andCone 3 beams at the LEH center. The color maps in all fourcases are the standard emission temperature map with theminimum set at T = 140 eV and the maximum at T = 220eV.

vs. 202 eV), in good agreement with the analytic powerbalance calculation. The sample temperature drop is 7eV in the case of the “nominal” pointing (186 eV vs. 193eV) at t = 1.0 ns and 6 eV lower in the case of the “singlering” pointing (182 eV vs. 188 eV). The slightly largertemperature decreases due to the presence of the capsulein the case of the wall-mounted samples arises from thelarge view factor of the capsule as seen by the sample,which is mounted at the midplane wall, and thus is quiteclose to the capsule. In the case of the nominal point-ing in which the capsule’s presence has a bigger effect onthe sample temperature, the capsule’s blocking of someof the laser hot spots as seen from the sample’s positionplays a role too.

We can also see in Fig. 7 that the effect of the cap-sule on the calculated radiation temperatures is less ex-treme at earlier times, when the capsule albedo and thehohlraum wall albedo have more similar values. Butother than these small differences in the DANTE vs. sam-ple radiation temperature and in the time-dependence ofthe effect of the capsule, the capsule’s effect is a uniformlowering of the radiation temperature in the hohlraumthat corresponds to roughly 2.5 percent, or roughly 10percent in radiation flux. By increasing the convertedlaser power by a corresponding 10 percent, the results ofthe simulations without the capsule are reproduced withthe capsule. This increase in power corresponds to in-creasing the XCE from 0.55 to 0.60. Thus the results of

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FIG. 7: Calculated radiation temperature vs. time for theVISRAD simulations shown in Fig. 6. The top panel is forthe “single ring” pointing while the bottom panel is for the“nominal” pointing. In each panel, we show the DANTE tem-perature for the empty (i.e. no capsule) hohlraum as a solidline and for the hohlraum containing a capsule as a dashedline. The radiation temperature seen by a wall-mounted sam-ple at the midplane is denoted by a dotted line for the emptyhohlraum and by a dash-dot line for the hohlraum with acapsule.

the view-factor simulations discussed in the remainder ofthis paper are applicable to hohlraums with capsules andslightly higher XCEs, although in detail, the temporal,spatial, and spectral dependencies will be affected by acapsule. If a high degree of accuracy is required in ana-lyzing these variations, then detailed simulations should

FIG. 8: The trend of radiation temperature as a function ofsample orientation for a planar sample located at the centerof a hohlraum. The angle plotted along the x-axis is the anglebetween the sample normal and the hohlraum axis, so that0 degrees is LEH-facing, while 90 degrees is wall-facing. Thefilled symbols are the results from t = 1.0 ns, while the opensymbols are from t = 100 ps. For comparison, the radiationtemperatures at these two times for a sample on the wall ofthe hohlraum at the midplane (discussed in Sec. II) are 188 eVand 129 eV (denoted by Xs); nearly identical to the centrallylocated, wall-facing (90 degree) results shown here. Finally,we note that the DANTE temperatures for these two timesare 202 eV and 143 eV, respectively. In this, and all otherfigures showing temperature trends in the remainder of thepaper, the left-hand axis refers to the values at t = 1 ns (solidsymbols), while the right-hand axis refers to the values att = 100 ps (open symbols).

be performed.

IV. EVOLUTION TO A HALFRAUM

Increasingly, indirect drive and related experimentsare performed in halfraums [10, 11], which are shortercylinders with only one LEH, sometimes referred to ashalf hohlraums, or single-ended hohlraums. Experimen-tal packages in halfraums are often mounted on the endof the cylinder, opposite the LEH. We might expect tosee similar effects to those we demonstrated in the previ-ous sections: spatial dependence of the drive propertieswithin a halfraum (both in terms of overall power andin terms of the spectral energy distribution) and, specifi-cally, differences between DANTE measurements and theradiation drive incident upon an experimental package.

Because a halfraum is essentially just half of ahohlraum, one expects its properties to not differ ap-

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FIG. 9: Comparison of the spectrum incident on a sampleat the center of a hohlraum (at t = 1.0 ns) when it is ori-ented toward the LEH (dashed line, 0 degree case in the pre-vious figure) vs. the spectrum when the sample is orientedtoward the hohlraum wall (solid line, 90 degree case in theprevious figure). The LEH-facing sample has a significantlyharder spectrum, though the radiation temperature onto eachis nearly identical (190 eV vs. 191 eV).

preciably from those of a hohlraum. There are only halfas many beams in a halfraum, but the wall area and theLEH area are also about half of that in a hohlraum. Onedifference between a hohlraum and a halfraum, for ex-periments with packages that are planar samples, is thata sample located at the midplane of a hohlraum is typ-ically mounted on the wall, or barrel, of the hohlraum,facing the opposite wall. In a halfraum, a planar packageis typically on the back end of the halfraum, facing theLEH. So there is a difference in the position and orien-tation of the sample, which will affect the relative viewfactors of hot spots and LEH, as compared to the case ofa planar sample mounted at the midplane of a hohlraum.In order to investigate the effect of sample position andorientation, we first repeated our initial hohlraum sim-ulations (without a capsule and with the simple “singlering” beam pointing such that both Cone 2 and Cone3 beams make a single ring of hot spots 480 µm fromthe LEH plane), but we located the planar sample inthe middle of the hohlraum, suspended where a capsulewould be. We performed four such simulations, varyingonly the sample orientation from wall facing to LEH fac-ing. The results of these four simulations are shown inFig. 8.

We find that the radiation temperature onto a planarsample at the center of the hohlraum is almost completelyindependent of sample orientation at t = 1.0 ns, whenthe albedo is high (α = 0.73). It is also nearly identicalto the radiation temperature on a wall-mounted planar

sample at the midplane. This result is relevant for ex-periments that, for example, investigate shock timing onwall-mounted packages and use the results to infer thedrive onto a capsule.

The variation among these five cases (four at the cen-ter of the hohlraum and one on the wall) is only 3 eV att = 1.0 ns, with no monotonic trend with orientation. In-deed, this result simply reflects the fact that cylindricalhohlraums, and their associated laser heating schemes,have been designed to generate a nearly uniform radia-tion drive onto a fuel capsule at their centers. The viewfactors of hot spots and cold LEHs change in concert witheach other as the sample orientation changes. However,although the radiation temperature is nearly independentof sample orientation, the spectral energy distribution isnot. In Fig. 9 we compare the spectrum incident upona sample facing the LEH with that incident on the samesample facing the hohlraum wall. The radiation temper-atures in these two cases are nearly identical (190 eV vs.191 eV), but the LEH-facing sample has a significantlyharder spectrum than the wall-facing sample (> 25%more flux at 2 keV; and if the gold M-band were explic-itly taken into account by the modeling, this differencecould be larger). This is because the LEH-facing samplehas more high-energy radiation incident upon it due toits larger hot-spot view factor and less lower-energy wallradiation due to its larger LEH view factor.

We also note, referring to Fig. 8, that there is a some-what larger dependence of radiation temperature on sam-ple orientation at early times, when the albedo is lower(α = 0.18 at t = 100 ps) than at late times. The ra-diation temperature is 6 eV higher for the LEH-facingsample than for the wall-facing sample at t = 100 ps.This is due to the fact that the wall-facing sample’s viewis dominated by a significantly cooler wall in a low-albedosituation.

Finally, it has been noticed that the DANTE temper-ature more closely tracks the sample temperature in ahalfraum configuration than in a similar hohlraum con-figuration [11]. Based on the above analysis, we see thatthis is not due to the difference in the sample position ororientation as one goes from a hohlraum to a halfraum.The sample radiation temperature does not change sig-nificantly as the sample is moved from the midplanehohlraum wall to the center of the hohlraum and turnedto face the LEH. In order to ascertain what accountsfor the better agreement between the DANTE tempera-ture and the sample temperature in the halfraum (recallthat this difference is about 15 eV in a hohlraum), weconstructed a model of a halfraum by simply taking ourhohlraum model having the sample in the center of thevolume and facing the LEH, and inserting a gold disk atthe midplane, to effectively divide the hohlraum in half,giving the resulting halfraum a length of 1150 µm. TheDANTE views from these two simulations are shown inFig. 10.

In the hohlraum case, the DANTE temperature is 202eV and the sample temperature is 190 eV (difference of

9

FIG. 10: The DANTE view at t = 1.0 ns of our originalhohlraum simulation (top) and the same view of a simulationthat differs only in having a gold disk dividing the hohlraumin half, effectively turning it into a halfraum (bottom). Thetemperature color scales are identical in the two figures. Notethat from this viewing angle, some of the laser hot spots onthe far side of the hohlraum, caused by beams entering thehohlraum through the far LEH, are visible, which is, of course,not the case with the dividing disk present.

28% in flux). In the halfraum case, the DANTE tem-perature is 193 eV and the sample temperature is 186eV (difference of 16% in flux). All temperatures arequoted for simulation time t = 1.0 ns. So, the pres-ence of the disk that divides the hohlraum in half affectsthe DANTE-measured drive by about twice as much as itaffects the sample drive. By inspecting Fig. 10 it is clearthat the proportionally larger drop in DANTE temper-ature in the halfraum case is due to the fact that in ahohlraum, DANTE sees some of the laser hot spot emis-sion from the far side of the hohlraum, which is causedby the beams entering through the far LEH. In the hal-fraum, DANTE sees instead wall reemission from the farend of the halfraum (or, equivalently, the disk at themidplane of the modified hohlraum in the case we have

presented here). In situations where low-angle beams,which cross the hohlraum midplane, are used, one seessimilar trends, with the low-angle beams hitting the backwall rather than the side wall of the halfraum. Such con-siderations are relevant to NIF [12] configurations, wherethere are a significant number of mid-plane-crossing low-angle beams.

V. BEAM POINTING WITHIN A

HALFRAUM

One straightforward way to try to control the driveproperties in a halfraum is to adjust the beam point-ing. Here we explore the dependence of the drive onto asample mounted on the back wall of a halfraum as thebeam pointing varies. We also monitor the DANTE tem-perature as a function of beam pointing, from the usualLEH view with a 37.4 degree angle to the halfraum axis.To simplify the situation, we revert to the pointing usedin the Decker et al. [4] experiments (the “single ring”pointing in which all 15 beams make a single ring of hotspots) and our initial modeling in Sec. II. The otherhalfraum properties are the same as those we have usedfor the previous modeling: variable XCE and albedo asdescribed earlier, a halfraum length of 1150 µm and adiameter of 1600 µm, and an LEH diameter of 1200 µm.All 15 beams are taken to have perfect square profilesover 1 ns and total energies of 500 J per beam. In all thesimulations presented in this section, the beams are fo-cused at the point at which they cross the halfraum axis.We make an exception for several beams in the simula-tion with the deepest beam pointing, where we had topull back the focus position slightly in order to keep thebeams from clipping the LEH lip.

We present four simulations, depicted in Fig. 11, inwhich the beam pointing varies by 150 µm for each sim-ulation. The second simulation (from the top), with thebeam pointing at the LEH plane, corresponds to the de-fault pointing used in the previous sections, with a hotspot distance of 480 µm from the LEH plane.

In Fig. 12 we show the trend of radiation tempera-ture on the back-wall sample along with the DANTEtemperature as a function of beam pointing. They aresimilar to what is seen in hohlraums (see Fig. 5) wheredeeper pointings generate higher temperatures by de-creasing LEH losses and positioning hot spots more favor-ably. The flattening out of the sample temperature trendwith the deepest pointing is due to the higher obliquity ofthe hot spots as seen by the sample. We note that, as de-tailed in the previous section, the DANTE temperatureexceeds the radiation temperature onto the sample by be-tween 5 and 10 eV at late times when the halfraum albedois high. But at earlier times, when the albedo is muchlower, the two temperatures are more similar. When thealbedo is low, the distinction between weak wall reemis-sion and cold LEH is minimal relative to the hot spots,so the sample seeing wall plus LEH and DANTE seeing

10

FIG. 11: Series of four halfraum simulations in which thebeam pointing was varied. The pairs of images show theDANTE view on the left and the view from behind the sam-ple on the far wall, or end cap, of the halfraum on the right;both at t = 1.0 ns. The top row has the beams pointed clos-est to the LEH, with the pointing moving in by 150 µm ateach simulation, moving down the figure. This series of sim-ulations has the beams pointed so that the hot spots make asingle ring, and the halfraum has a three-quarter LEH.

solely wall give similar radiation temperatures.

It is clear from these beam pointing simulations, andespecially from inspecting the left-hand column of Figs.11, that the LEH lip can play an important role, as itaffects the DANTE view factors in addition to the ef-fect it has on keeping reemitted radiation from escapingout the LEH. To investigate this quantitatively, we haveperformed another series of four view-factor simulations.These are analogous to the previous set discussed in thissection (see Fig. 11), where all 15 beams are pointed toform a single ring of hot spots, and in each successive

FIG. 12: The radiation temperature on a sample mountedon the end of a halfraum (circles) and measured by DANTE(squares) for the four different beam pointings shown in Fig.11 (three-quarter LEH, hot spots in single ring) at two dif-ferent simulation times: t = 1.0 ns (filled symbols; left-handaxis) and t = 100 ps (open symbols; right-hand axis).

simulation, all the beams are moved 150 µm further intothe halfraum. The only difference between these newsimulations and the original ones is that in the new ones,there is no LEH lip. That is, the LEH diameter is 100%of the halfraum diameter.

The results of this series of simulations are shown inFig. 13, where the emission temperature color maps of thetargets are displayed, and in Fig. 14, where the trends ofsample and DANTE radiation temperature are shown.The removal of the LEH lip has several effects. TheDANTE temperatures are lower, and somewhat less de-pendent on the beam pointing. This appears to be be-cause the portion of the halfraum wall nearest the LEHis much colder in these simulations than in those withan LEH lip. In the simulations with the lip (i.e. three-quarter LEH), the DANTE temperature increases moredramatically as the pointing becomes deeper because thehot spots are moving into the DANTE field of view andout of the shadow of the lip. Here, the hot spots are al-ready in the DANTE field of view even for shallow point-ings. As the beams are pointed further in, the DANTEview factor of hot spots increases, but this effect is can-celed by the larger size of the cool wall region near theLEH.

The sample radiation temperature is somewhat lower(by as much as 10 eV) in these simulations without thelip compared to those with the LEH lip, due to increasedlosses through the LEH. The trend of increased sampletemperature with deeper pointing is apparent in thesesimulations without the LEH lip, as it was in the sim-ulations with the lip. The trend is somewhat strongerin the simulations without the lip, likely because the in-

11

FIG. 13: Series of four halfraum simulations in which thebeam pointing was varied. These are identical to the seriesshown in Fig. 11, except that the LEH is larger in these tar-gets, with a diameter equal to the diameter of the halfraumitself (i.e. no lip on the LEH). The pairs of images show theDANTE view on the left and the view from behind the sampleon the far wall, or end cap, of the halfraum on the right; bothat t = 1.0 ns. The top row has the beams pointed closestto the LEH, with the pointing moving in by 150 µm at eachsimulation, moving down the figure.

creased LEH losses are stronger for the shallower point-ing cases. In summary, the sample temperature dropsmore than the DANTE temperature due to the absenceof the LEH lip because the sample sees a bigger cold LEHbut DANTE sees more of the hot spots than in the casewith the LEH lip, which partially compensates for theincreased LEH losses.

We performed a final series of simulations with varyingbeam pointing, but this time with a more natural point-ing configuration, in which the aim point of both Cones

FIG. 14: The radiation temperature on a sample mountedon the end of a halfraum (circles) and measured by DANTE(squares) for the four different beam pointings shown in Fig.13 at two different simulation times: t = 1.0 ns (filled symbols;left-hand axis) and t = 100 ps (open symbols; right-handaxis). In these simulations there is no LEH lip (i.e. 100%LEH) and the beams are pointed to form a single ring of hotspots.

2 and 3 are the same, causing two separate rings of hotspots on the walls of the halfraum. We also revert backto the standard, three-quarter LEH for this series. Thenominal pointing in this case has all 15 beams pointed(and focused) at the LEH center. This makes a ring ofhot spots (from Cone 3) at 480 µm from the LEH planeand another ring (from Cone 2) at 890 µm from the LEHplane (see the second row of Fig. 15). As in the previoustwo sets of simulations, we vary the pointing by movingall the beams inward by 150 µm and then by 300 µm, andalso calculate a case in which all the beams are pulled out150 µm from this nominal pointing.

The results of this series of simulations are summa-rized in Figs. 15 and 16. The general trends shown pre-viously are also seen in this series of calculations. Thedrive temperature onto the sample is relatively indepen-dent of pointing, except for the most extreme cases, inwhich it is a little cooler. This is because the effect ofthe obliquity of the hot spot view is even more extreme,with the Cone 2 beams pointed further into the halfraum.The DANTE temperatures are also quite independent ofbeam pointing, and modestly higher than the sample ra-diation temperatures (more so at the later times, whenthe wall albedo is higher).

12

FIG. 15: Final series of four halfraum simulations, in whichthe beam pointing was varied. The beam pointing here givestwo separate rings for Cones 2 and 3, respectively, and we re-vert to the standard three-quarter LEH. The beams are movedinward by 150 µm each step down the figure, with the sec-ond row representing the nominal pointing (all beams pointedat the center of the LEH). The left hand column shows theDANTE view, the right hand column shows the sample view.The colors represent emission temperatures at t = 1.0 ns.

VI. OPTIMIZING HALFRAUM GE-

OMETRY

The results from the previous section can be used tomaximize the radiation drive onto a sample mounted onthe back wall of a halfraum, as well as to relate radiationdiagnostics from DANTE to the sample drive properties.In this section, we investigate the dependence of driveproperties on halfraum length and also on the presence ofinternal LEH shields as well as a foil just outside the LEH.For simplicity, we keep the halfraum diameter (1600 µm)

FIG. 16: Temperature as a function of pointing for the thirdset of simulations described in this section (see Fig. 15), withthe two beam cones making two different rings of hot spots,and using the three-quarter LEH. The solid symbols are froma simulation time of t = 1.0 ns (left-hand axis) while the opensymbols are from t = 100 ps (right-hand axis). The squaresare DANTE temperatures and the circles are sample radiationtemperatures.

and LEH diameter (1200 µm) the same for these simula-tions and also do not vary the beam properties. In thisfirst set of simulations, the beam pointing is always at theLEH center (with the beams all focused at this point aswell). Thus, as the halfraum length changes, the distanceof the hot spots from the sample also changes.

In Fig. 17 we show a series of four simulations in whichthe halfraum length is varied from 1000 µm to 1450 µmin steps of 150 µm. In Fig. 18 we plot DANTE and sam-ple temperatures at two different simulation times as afunction of halfraum length. These temperatures are rel-atively independent of length, with only a slight decreasein radiation temperature for the longer halfraums. Thetendency toward lower temperatures due to the greaterwall area in the longer halfraums must be offset by fewerradiation losses out the LEH, and for the sample, thesmaller LEH solid angle as the halfraum lengthens alsotends to offset the increased wall losses. The drop in thesample radiation temperature for the shortest halfraumsis due to the obliquity of the hot spots as seen from thesample, especially the Cone 2 spots.

To investigate whether the slight decrease in the radia-tion temperature of the back wall mounted sample is pri-marily due to its distance from the hot spots, we repeatedthe previous series of experiments, but with the beampointing adjusted in each case to keep the hot spots’ dis-tance from the sample constant as the halfraum lengthwas adjusted. For this series of calculations, we kept thenominal (LEH centered) pointing for the standard hal-fraum length of 1150 µm. However, for each of the other

13

FIG. 17: Series of four halfraum simulations in which thelength of the halfraum was varied. From top to bottom, thehalfraum lengths are 1000, 1150, 1300, and 1450 µm. Thebeam pointing and focus was at the LEH center in all cases.The left hand column shows the DANTE view and the righthand column the sample view. The colors represent emissiontemperatures taken from t = 1.0 ns in each simulation.

three halfraum lengths, we moved all 15 beams eitherin or out according to the halfraum length so that thepointings, and thus the hot spots’ positions, were alwaysthe same distance from the sample. Thus, for the 1000µm long halfraum, the beam pointing was 150 µm out-side of the LEH, at the halfraum axis. For the 1300 µmhalfraum, the pointing was 150 µm inside the LEH, andfor the 1450 µm halfraum, it was 300 µm inside. For allbut the longest halfraum, all the beams were focused atthe pointing position. For the longest halfraum, we hadto focus the beams closer to the LEH plane, to preventbeam clipping on the LEH lip.

The results of this series of simulations are shown in

FIG. 18: Temperature as a function of halfraum length for thefour simulations shown in Fig. 17, with all simulations havingidentical beam pointings with respect to the LEH. The solidsymbols are from a simulation time of t = 1.0 ns (left-handaxis) while the open symbols are from t = 100 ps (right-handaxis). The squares are DANTE temperatures and the circlesare sample radiation temperatures.

Figs. 19 and 20. The primary result is that the sampletemperature is almost totally independent of halfraumlength (at both 100 ps and 1 ns). This is, of course,counter to the expectations of standard hohlraum tem-perature power balance analysis, which would predictlower temperatures as the halfraum was lengthened (asis seen in the first set of simulations discussed in thissection). Clearly, the fact that the sample’s view fac-tor of hot spots is the same in each of these four cases(because the pointing is constant relative to the sampleitself) is much more important than the addition of ex-tra wall area as the halfraum is lengthened. Furthermore,the LEH subtends a smaller solid angle as seen from thelocation of the hot spots in the longer halfraums, so LEHlosses are minimized, even as wall losses increase. TheDANTE temperature decreases somewhat with increas-ing halfraum length because the wall in the DANTE fieldof view includes contributions from regions farther fromthe hot spots when the halfraum is longer, and these wallregions are colder, as there is a negative axial tempera-ture gradient associated with the hot spots.

In order to maximize the radiation drive onto a sam-ple, or generally in a hohlraum or halfraum, extra wallsor barriers or other complex geometries can be employed.Boosts of the drive onto a capsule have been demon-strated via the use of walls on the interior of hohlraumsthat block the capsule’s view of the LEH [13].

We performed a simulation to investigate the effectsof such “LEH shields.” Again using a standard size(2300 × 1600 µm) hohlraum with three-quarter LEHs,we put two 600 µm diameter gold disks centered on the

14

FIG. 19: Series of four halfraum simulations in which thelength of the halfraum was varied. From top to bottom,the halfraum lengths are 1000, 1150, 1300, and 1450 µm.The beam pointing and focus was varied along with halfraumlength, so the distance from the hot spots to the sample wasthe same for all four simulations. The case shown in the sec-ond row (for a halfraum of standard length, l = 1150 µm), isidentical to that shown in the previous set of simulations (sec-ond row of Fig. 17), but the beam pointing is 150 µm outsideof the LEH for the shortest halfraum, shown in the top row,and 150 µm and 300 µm inside the LEH for the bottom twocases, respectively. The left hand column shows the DANTEview and the right hand column the sample view. The colorsrepresent emission temperatures taken from t = 1.0 ns in eachsimulation.

hohlraum axis 600 µm from the hohlraum midplane. Weused the nominal beam pointing, with all 15 beams oneach side of the hohlraum pointed and focused at the cen-ter of the LEH. As expected, and shown experimentally,these LEH shields boost the temperature at the mid-plane of the hohlraum by blocking much of the area of

FIG. 20: Temperature as a function of halfraum length, wherethe beam pointing is changed along with halfraum length,such that the hot spots’ distance from the sample mountedon the back wall is always the same (mean hot spot distanceof 530 µm from the back wall, measured along the barrel).The solid symbols are from a simulation time of t = 1.0 ns(left-hand axis) while the open symbols are from t = 100 ps(right-hand axis). The squares are DANTE temperatures andthe circles are sample radiation temperatures.

the LEHs as seen by a sample and also by the hot spots,decreasing the effective view factor of cold LEH and pre-venting much of the radiation losses out the LEH. Theusual emission temperature color maps from two differentviews are shown for this simulation in Fig. 21.

We monitored the radiation temperature in this sim-ulation on a sample at the center of the hohlraum (andfacing one of the LEHs) as well as on a midplane wall-mounted sample. The radiation temperature on thesetwo samples never varied by more than 2 eV (135 eV vs.135 eV at t = 100 ps and 197 eV vs. 195 eV at t = 1ns). In the simulation without the shields, the sampletemperatures are nearly identical at early times (134 eVand 135 eV at t = 100 ps for the hohlraum-center andwall-mounted samples, respectively) but are somewhatlower at later times (190 eV and 193 eV at t = 1 ns).The lack of effect of the LEH shields on the sample tem-perature at early times is due to the fact that the shieldsthemselves are not yet hot enough to emit significant ra-diation; they are nearly as cold as the LEHs that theyblock. But at late times, the shields boost the temper-ature on a sample at the center of the hohlraum by 7eV, corresponding to 16% in flux). The DANTE tem-perature is significantly lower in the simulation with theshields (197 eV at t = 1 ns vs. 207 eV at the same simula-tion time in the case without the shields). As can clearlybe seen in the simulation (Fig. 21), the lower DANTEtemperature is due the fact that the back of the shieldis in the DANTE view, blocking this diagnostic’s view

15

FIG. 21: Emission temperature color maps at, t = 1 ns, ofthe hohlraum simulation with the LEH shields (top row) com-pared to an identical simulation without shields (bottom row;same simulation as that shown in the top panel of Fig. 5). Theleft column shows the usual DANTE view, while the right col-umn shows a view from near the hohlraum midplane, lookingtoward one of the LEHs.

of some hot spots and wall reemission. We note that,at least in this particular simulation we have discussed,the radiation temperature on a sample at the hohlraumcenter and the DANTE temperature are identical.

A strategy similar to the use of LEH shields mightinvolve putting metal foils outside the LEH to absorbradiation lost out the LEH and reemit it back into thehohlraum or halfraum. In Fig. 22 we show an exampleof this scheme, in which a circular foil with a diameter of700 µm is hung 500 µm outside the LEH. One potentialadvantage of this scheme is that a foil on the exterior canbe irradiated with unused beams from the other (non-LEH-facing) side of the target chamber to provide anadditional source of x-rays to heat the halfraum.

We performed two simulations of the halfraum withthe foil in the configuration described above, and usingthe nominal pointing (all 15 beams pointed at the centerof the LEH plane) and halfraum size (l = 1150 µm). Inone, we do not irradiate the foil at all, and in the other,we irradiate the foil with all ten Cone 3 beams from theother side of the halfraum, using the same power profileas the halfraum beams (1 ns square pulses with 500 Jper beam). It is easily seen from the color map in Fig. 22that this additional source of radiation makes the entirehalfraum hotter. In Fig. 23 we compare the spectra in-cident on the sample (mounted as usual on the center ofthe back wall of the halfraum) from the two cases withthe foil (irradiated and not) to the standard case withoutthe foil. It can be seen from this figure that while sim-ply adding the foil makes very little difference (sample

FIG. 22: Two halfraum simulations with a metal foil justoutside the LEH. In the simulation shown in the top twopanels, there are no beams onto the foil. The foil simplyacts to absorb and reemit radiation that exits through theLEH. In the bottom two panels, there are ten beams onto thefoil, which significantly increases the radiation flux inside thehalfraum. All the snapshots show emission temperatures att = 1.0 ns.

radiation temperature of 187 eV vs. 185.5 eV, or 3% influx), irradiating the foil makes a large difference, rais-ing the radiation temperature on the sample to 207 eV(representing a 55% increase in total flux), and roughlydoubling the radiation flux at 2 keV.

VII. CONCLUSIONS

We have presented results from numerical view-factorsimulations performed to investigate the variation of radi-ation conditions as a function of spatial, geometrical, andbeam pointing conditions for hohlraums and halfraumsat OMEGA. In addition, we have presented results show-ing sometimes significant differences in the hohlraum walltemperatures viewed by DANTE and the radiation drivetemperatures seen by experimental packages attached tothe hohlraum or halfraum walls. Because the radiativeflux, and thus the heating, scales as the fourth power ofthe temperature, even modest differences in wall tem-peratures can be significant. View-factor simulations,such as those presented here, provide a means of sim-ulating hohlraum radiation characteristics and interpret-ing wall emission measurements (e.g., DANTE), and canbe of value in designing and interpreting experiments atOMEGA and future experiments at NIF.

We find, specifically, from several series of simulations,that the radiation drive onto a sample can differ substan-tially from that measured by an absolutely calibrated x-ray detector, like DANTE, even when the diagnostic line

REFERENCES 16

FIG. 23: Comparison of spectra incident on the center of thesample in our standard (l = 1150 µm) halfraum at t = 1.0 ns,with the standard beam pointing. The dotted line representsthe simulation with no foil, the dashed line (nearly coincidentwith the dotted line) represents the simulation with a foiloutside the LEH, and the solid line is from the simulationwith the foil heated by ten beams.

of sight is through an LEH. This is especially true inhohlraums, as compared to halfraums, and at late times(when wall albedos are high). In the standard hohlraumsimulations we carried out, the radiation temperature ona sample at the hohlraum midplane is roughly 15 eVlower than the DANTE temperature. In standard hal-fraum configurations, there is good agreement betweenDANTE temperatures and radiation temperatures ontoa sample mounted at the center of the back wall (roughlya 5 eV discrepancy at 200 eV). This better agreement isprimarily due to the fact that in a hohlraum, the DANTEtemperature is boosted with respect to a halfraum be-cause DANTE sees some of the hot spots on the far sideof the hohlraum, from beams entering from the oppositeside. We also find that midplane radiation temperaturesin hohlraums are very similar to radiation temperaturesonto a sample suspended at the center of a hohlraum,and further, that the orientation of such a sample hasvery little effect on the radiation temperature.

It was also shown that even when radiation tempera-tures between two different samples, or between a sam-ple and DANTE, are very similar, the respective spectralenergy distributions can differ significantly. The primarytrend we found is that incident spectra are harder thanthe equivalent Planckian spectra having the same radi-ation temperature. Another, milder, trend is that thespectrum onto a sample tends to be harder than thatseen by DANTE.

Variations in beam pointing and halfraum length were

found to have relatively little effect, generally, on eitherthe sample radiation temperature or the DANTE tem-perature, except in extreme cases. The mean laser spotposition can be varied anywhere from roughly 400 µmto 800 µm from the LEH plane in a standard halfraumwithout changing either the DANTE temperature or thedrive temperature onto a sample more than a few eV.And a 1600 µm diameter halfraum will provide maximaldrive temperatures with nominal beam pointing when thehalfraum has a length anywhere between 1100 and 1400µm. However, the size of the LEH can have a signifi-cant effect on both DANTE and sample temperatures.Furthermore, the presence of a capsule in a hohlraumwill lower both the DANTE temperature and the sampletemperature in a predictable way due to increased lossesinto the low-albedo capsule. Finally, the drive onto asample can be increased significantly by the inclusion ofLEH shields (which also have the effect of lowering theDANTE temperature, bringing it into much closer agree-ment with the sample temperature) or by irradiating afoil placed just outside the LEH of a halfraum.

Acknowledgments

We are grateful for support through grant DE-FG03-OOSF22023 (from the DOE/NLUF program) toPrism Computational Sciences, and Research Corpora-tion grant CC5489 to Swarthmore College. We alsothank Rick Olson for useful discussions and Dave Con-ners for performing some initial calculations.

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